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Article Dans Une Revue Discrete Applied Mathematics Année : 2015

Efficiently decomposing, recognizing and triangulating hole-free graphs without diamonds

Résumé

A graph is hole- and diamond-free (HD-free) if none of its induced subgraphs is isomorphic to a chordless cycle of length at least five or to a diamond. Using the clique separator approach and the simple structure of atoms of HD-free graphs, we show how to recognize HD-free graphs in time O(n(2)). One of the main tools is Lexicographic Breadth-First Search (LexBFS); we give two new properties of LexBFS which are essential for reaching the time bound and which hold for any graph. Moreover, we find minimal triangulations of HD-free graphs in time O(n(2)), introducing efficient algorithms for the minimal triangulation of matched co-bipartite graphs and chordal bipartite graphs

Domaines

Autre [cs.OH]

Dates et versions

hal-01323853 , version 1 (31-05-2016)

Identifiants

Citer

Anne Berry, Andreas Brandstädt, Vassilis Giakoumakis, Frédéric Maffray. Efficiently decomposing, recognizing and triangulating hole-free graphs without diamonds. Discrete Applied Mathematics, 2015, 184, pp.50-61. ⟨10.1016/j.dam.2014.11.018⟩. ⟨hal-01323853⟩
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